今天介绍DBN的内容，其中关键部分都是(Restricted Boltzmann Machines, RBM)的步骤，所以先放一张rbm的结构，帮助理解
(图来自baidu的一个讲解ppt)
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照例，我们首先来看一个完整的DBN的例子程序：
这是\tests\test_example_DBN.m 中的ex2
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- //train dbn
- dbn.sizes = [100 100];
- opts.numepochs = 1;
- opts.batchsize = 100;
- opts.momentum = 0;
- opts.alpha = 1;
- dbn =dbnsetup(dbn, train_x, opts); //here！！！
- dbn = dbntrain(dbn, train_x, opts); //here！！！
- //unfold dbn to nn
- nn = dbnunfoldtonn(dbn, 10); //here！！！
- nn.activation_function = ‘sigm‘;
- //train nn
- opts.numepochs = 1;
- opts.batchsize = 100;
- nn = nntrain(nn, train_x, train_y, opts);
- [er, bad] = nntest(nn, test_x, test_y);
- assert(er < 0.10, ‘Too big error‘);
//train dbn dbn.sizes = [100 100]; opts.numepochs = 1; opts.batchsize = 100; opts.momentum = 0; opts.alpha = 1; dbn =dbnsetup(dbn, train_x, opts); //here！！！ dbn = dbntrain(dbn, train_x, opts); //here！！！ //unfold dbn to nn nn = dbnunfoldtonn(dbn, 10); //here！！！ nn.activation_function = ‘sigm‘; //train nn opts.numepochs = 1; opts.batchsize = 100; nn = nntrain(nn, train_x, train_y, opts); [er, bad] = nntest(nn, test_x, test_y); assert(er < 0.10, ‘Too big error‘);
其中的过程简单清晰明了，就是dbnsetup(),dbntrain()以及dbnunfoldtonn()三个函数
最后fine tuning的时候用了（一）里看过的nntrain和nntest，参见（一）
\DBN\dbnsetup.m
这个实在没什么好说的，
直接分层初始化每一层的rbm(受限波尔兹曼机(Restricted Boltzmann Machines, RBM)) 同样，W,b,c是参数，vW,vb,vc是更新时用到的与momentum的变量，见到代码时再说
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- for u = 1 : numel(dbn.sizes) - 1
- dbn.rbm{u}.alpha = opts.alpha;
- dbn.rbm{u}.momentum = opts.momentum;
- dbn.rbm{u}.W = zeros(dbn.sizes(u + 1), dbn.sizes(u));
- dbn.rbm{u}.vW = zeros(dbn.sizes(u + 1), dbn.sizes(u));
- dbn.rbm{u}.b = zeros(dbn.sizes(u), 1);
- dbn.rbm{u}.vb = zeros(dbn.sizes(u), 1);
- dbn.rbm{u}.c = zeros(dbn.sizes(u + 1), 1);
- dbn.rbm{u}.vc = zeros(dbn.sizes(u + 1), 1);
- end
for u = 1 : numel(dbn.sizes) - 1
dbn.rbm{u}.alpha = opts.alpha;
dbn.rbm{u}.momentum = opts.momentum;
dbn.rbm{u}.W = zeros(dbn.sizes(u + 1), dbn.sizes(u));
dbn.rbm{u}.vW = zeros(dbn.sizes(u + 1), dbn.sizes(u));
dbn.rbm{u}.b = zeros(dbn.sizes(u), 1);
dbn.rbm{u}.vb = zeros(dbn.sizes(u), 1);
dbn.rbm{u}.c = zeros(dbn.sizes(u + 1), 1);
dbn.rbm{u}.vc = zeros(dbn.sizes(u + 1), 1);
end
\DBN\dbntrain.m
应为DBN基本就是把rbm当做砖块搭建起来的，所以train也很简单
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- function dbn = dbntrain(dbn, x, opts)
- n = numel(dbn.rbm);
- //对每一层的rbm进行训练
- dbn.rbm{1} = rbmtrain(dbn.rbm{1}, x, opts);
- for i = 2 : n
- x = rbmup(dbn.rbm{i - 1}, x);
- dbn.rbm{i} = rbmtrain(dbn.rbm{i}, x, opts);
- end
- end
function dbn = dbntrain(dbn, x, opts)
n = numel(dbn.rbm);
//对每一层的rbm进行训练
dbn.rbm{1} = rbmtrain(dbn.rbm{1}, x, opts);
for i = 2 : n
x = rbmup(dbn.rbm{i - 1}, x);
dbn.rbm{i} = rbmtrain(dbn.rbm{i}, x, opts);
end
end
首先映入眼帘的是对第一层进行rbmtrain()，后面每一层在train之前用了rbmup，
rbmup其实就是简单的一句sigm(repmat(rbm.c‘, size(x, 1), 1) + x * rbm.W‘);
也就是上面那张图从v到h计算一次，公式是Wx+c
接下来是最关键的rbmtrain了：
\DBN\rbmtrain.m
代码如下，说明都在注释里
论文参考：【1】Learning Deep Architectures for AI 以及
【2】A Practical Guide to Training Restricted Boltzmann Machines
你可以和【1】里面的这段伪代码对应一下
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- for i = 1 : opts.numepochs //迭代次数
- kk = randperm(m);
- err = 0;
- for l = 1 : numbatches
- batch = x(kk((l - 1) * opts.batchsize + 1 : l * opts.batchsize), :);
- v1 = batch;
- h1 = sigmrnd(repmat(rbm.c‘, opts.batchsize, 1) + v1 * rbm.W‘); //gibbs sampling的过程
- v2 = sigmrnd(repmat(rbm.b‘, opts.batchsize, 1) + h1 * rbm.W);
- h2 = sigm(repmat(rbm.c‘, opts.batchsize, 1) + v2 * rbm.W‘);
- //Contrastive Divergence 的过程
- //这和《Learning Deep Architectures for AI》里面写cd-1的那段pseudo code是一样的
- c1 = h1‘ * v1;
- c2 = h2‘ * v2;
- //关于momentum，请参看Hinton的《A Practical Guide to Training Restricted Boltzmann Machines》
- //它的作用是记录下以前的更新方向，并与现在的方向结合下，跟有可能加快学习的速度
- rbm.vW = rbm.momentum * rbm.vW + rbm.alpha * (c1 - c2) / opts.batchsize;
- rbm.vb = rbm.momentum * rbm.vb + rbm.alpha * sum(v1 - v2)‘ / opts.batchsize;
- rbm.vc = rbm.momentum * rbm.vc + rbm.alpha * sum(h1 - h2)‘ / opts.batchsize;
- //更新值
- rbm.W = rbm.W + rbm.vW;
- rbm.b = rbm.b + rbm.vb;
- rbm.c = rbm.c + rbm.vc;
- err = err + sum(sum((v1 - v2) .^ 2)) / opts.batchsize;
- end
- end
for i = 1 : opts.numepochs //迭代次数
kk = randperm(m);
err = 0;
for l = 1 : numbatches
batch = x(kk((l - 1) * opts.batchsize + 1 : l * opts.batchsize), :);
v1 = batch;
h1 = sigmrnd(repmat(rbm.c‘, opts.batchsize, 1) + v1 * rbm.W‘); //gibbs sampling的过程
v2 = sigmrnd(repmat(rbm.b‘, opts.batchsize, 1) + h1 * rbm.W);
h2 = sigm(repmat(rbm.c‘, opts.batchsize, 1) + v2 * rbm.W‘);
//Contrastive Divergence 的过程
//这和《Learning Deep Architectures for AI》里面写cd-1的那段pseudo code是一样的
c1 = h1‘ * v1;
c2 = h2‘ * v2;
//关于momentum，请参看Hinton的《A Practical Guide to Training Restricted Boltzmann Machines》
//它的作用是记录下以前的更新方向，并与现在的方向结合下，跟有可能加快学习的速度
rbm.vW = rbm.momentum * rbm.vW + rbm.alpha * (c1 - c2) / opts.batchsize;
rbm.vb = rbm.momentum * rbm.vb + rbm.alpha * sum(v1 - v2)‘ / opts.batchsize;
rbm.vc = rbm.momentum * rbm.vc + rbm.alpha * sum(h1 - h2)‘ / opts.batchsize;
//更新值
rbm.W = rbm.W + rbm.vW;
rbm.b = rbm.b + rbm.vb;
rbm.c = rbm.c + rbm.vc;
err = err + sum(sum((v1 - v2) .^ 2)) / opts.batchsize;
end
end
\DBN\dbnunfoldtonn.m
DBN的每一层训练完成后自然还要把参数传递给一个大的NN，这就是这个函数的作用
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- function nn = dbnunfoldtonn(dbn, outputsize)
- %DBNUNFOLDTONN Unfolds a DBN to a NN
- % outputsize是你的目标输出label，比如在MINST就是10，DBN只负责学习feature
- % 或者说初始化Weight，是一个unsupervised learning，最后的supervised还得靠NN
- if(exist(‘outputsize‘,‘var‘))
- size = [dbn.sizes outputsize];
- else
- size = [dbn.sizes];
- end
- nn = nnsetup(size);
- %把每一层展开后的Weight拿去初始化NN的Weight
- %注意dbn.rbm{i}.c拿去初始化了bias项的值
- for i = 1 : numel(dbn.rbm)
- nn.W{i} = [dbn.rbm{i}.c dbn.rbm{i}.W];
- end
- end
function nn = dbnunfoldtonn(dbn, outputsize)
%DBNUNFOLDTONN Unfolds a DBN to a NN
% outputsize是你的目标输出label，比如在MINST就是10，DBN只负责学习feature
% 或者说初始化Weight，是一个unsupervised learning，最后的supervised还得靠NN
if(exist(‘outputsize‘,‘var‘))
size = [dbn.sizes outputsize];
else
size = [dbn.sizes];
end
nn = nnsetup(size);
%把每一层展开后的Weight拿去初始化NN的Weight
%注意dbn.rbm{i}.c拿去初始化了bias项的值
for i = 1 : numel(dbn.rbm)
nn.W{i} = [dbn.rbm{i}.c dbn.rbm{i}.W];
end
end
最后fine tuning就再训练一下NN就可以了
总结
还是那句话，本文只是梳理一下学习路线，具体的东西还是要靠paper
dbn主要的关键就是rbm，推荐几篇经典的文章吧，rbm可是Hinton的宝贝啊
其中涉及到MCMC，Contrastive divergence，感觉比Autoencoder难理解多了
[1] An Introduction to Restricted Boltzmann Machines
[2] Learning Deep Architectures for AI Bengio大作啊
[3] A Practical Guide to Training Restricted Boltzmann Machines 上面提到过，比较细致
[4] A learning Algorithm for Boltzmann Machines Hinton的